With lots of Apple (AAPL -1.22%) followers panicking about the success of Apple's new iPhones (for no good reason, in my opinion) investors are looking for any source of comfort. Apple won't report its quarterly earnings until Oct. 28, so we won't get the full story on iPhone sales until then.

The iPhone 5S is Apple's new high-end model. Photo: Apple.

Fortunately for worried Apple investors, Verizon (VZ 0.90%) provided some good news in its quarterly earnings report on Thursday. Of the 7.6 million smartphones activated by Verizon in the third quarter, 51% were iPhones.

This implies that Verizon sold approximately 3.9 million iPhones in the quarter. That's a very strong number, and it suggests Apple will post a massive year-over-year increase in iPhone shipments for the three-month period that ended in September.

A big player
As the largest wireless carrier in Apple's largest market, Verizon is a key partner for Apple. (AT&T still has the most iPhone users, though, due to its position as the original U.S. iPhone carrier.) In the first half of this year, roughly 11% of all worldwide iPhone activations were on the Verizon network.

Verizon is becoming even more important to Apple over time. The iPhone has been gradually gaining share from Android and BlackBerry devices at Verizon, while Verizon has been winning market share away from AT&T. In last year's quarter ending in September, the iPhone accounted for 46% of all smartphone sales at Verizon, but this year the iPhone's share increased to 51%. This helped drive Verizon's iPhone activations up by roughly 25% year over year, from 3.1 million to 3.9 million.

What does it mean for Apple?
Since Verizon's share of worldwide iPhone activations has been fairly stable recently, it is possible to use Verizon's sales numbers to get a rough estimate of how many iPhones Apple sold last quarter. As noted above, in the first two quarters of 2013, Verizon activated 11% of all iPhones sold worldwide. In last year's quarter that closed in September, Verizon had a 12% share.

There are a few factors that could impact Verizon's share of total iPhone activations this quarter. First, as noted before, Verizon has been gaining share within the U.S. mobile market, and the iPhone has been gaining share within Verizon. These factors would tend to increase Verizon's share of worldwide iPhone activations.

On the other hand, this year Apple for the first time launched its new iPhone 5s and iPhone 5c handsets in China at the same time as the U.S. This means that a higher percentage of Apple's iPhone sales may have come from international markets last quarter compared to a year ago. That would reduce Verizon's share of worldwide iPhone sales.

The iPhone 5C. Photo: Apple.

Overall, these two factors should balance each other out and Verizon's 3.9 million iPhones will likely represent 11%-12% of worldwide iPhone sales for last quarter. That implies that Apple may have sold 32 million-35 million iPhones last quarter, which would be 20%-30% higher than the 26.9 million sold in last year's corresponding three-month period. Anything in that range would be a great result, especially since Apple did not release a lower-margin "cheap" iPhone to gain market share.

Foolish conclusion
It's important to remember that there are a lot of moving parts involved in Apple's quarterly iPhone sales tally. For instance, it's possible that Verizon had a better initial supply of the new iPhones this year compared to last year. Therefore, investors shouldn't assume that a 25% increase at Verizon translates directly to a 25% increase in worldwide iPhone sales.

Nevertheless, Verizon's strong iPhone activation numbers -- combined with Apple's big opening weekend sales tally -- should make investors comfortable that Apple sold plenty of iPhones last quarter. Since the iPhone is responsible for the majority of Apple's revenue and profit, this bodes well for the company's quarterly earnings. There's no need to worry about Apple: It's doing just fine!